华东师范大学学报（自然科学版） >

2020 , Vol. 2020 >Issue 2: 35 - 40

DOI: https://doi.org/10.3969/j.issn.1000-5641.201911007

数学

赋Φ-Amemiya范数的Orlicz空间包含序渐进等距c0复本

  • 崔云安 ,
  • 安莉丽
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  • 哈尔滨理工大学 理学院, 哈尔滨　150080
崔云安,男,教授.研究方向为泛函分析.E-mail:cuiya@hrbust.edu.cn;安莉丽,女,硕士研究生.研究方向为泛函分析.E-mail:1468126191@qq.com

收稿日期: 2019-01-24

  网络出版日期: 2020-03-16

基金资助

国家自然科学基金（11871181，11701125）

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The Orlicz space equipped with the Φ-Amemiya norm contains an order asymptotically isometric copy of c0

  • CUI Yun'an ,
  • AN Lili
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  • College of Science, Harbin University of Science and Technology, Harbin　150080, China

Received date: 2019-01-24

  Online published: 2020-03-16

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摘要

在Orlicz空间中, 我们引进了一个与Luxemburg范数等价的新范数—赋Φ-Amemiya范数: ${\left\| x \right\|_{\Phi ,{\Phi _1}}} = \inf \left\{ {\frac{1}{k}\left( {1 + \Phi \left( {{{ I}_{{\Phi _1}}}\left( {kx} \right)} \right)} \right)} \right\}$. 并证明了由此范数构成的Orlicz函数空间$\left\{ {{L_{\Phi ,{\Phi _{\rm{1}}}}},{{\left\| \cdot \right\|}_{\Phi ,{\Phi _1}}}} \right\}$是Banach空间. 据此得到了赋Φ-Amemiya范数的Orlicz空间包含序渐近等距c0复本的条件.

关键词： Orlicz空间; Amemiya范数; Δ2条件; c0的序渐近等距复本

本文引用格式

崔云安 , 安莉丽 . 赋Φ-Amemiya范数的Orlicz空间包含序渐进等距c0复本[J]. 华东师范大学学报（自然科学版）, 2020 , 2020(2) : 35 -40 . DOI: 10.3969/j.issn.1000-5641.201911007

Abstract

In Orlicz space, a new norm that is equivalent to the Luxemburg norm is introduced. It is called the Φ-Amemiya norm: ${\left\| x \right\|_{\Phi ,{\Phi _1}}} = \inf \left\{ {\frac{1}{k}\left( {1 + \Phi \left( {{{ I}_{{\Phi _1}}}\left( {kx} \right)} \right)} \right)} \right\}$. It is shown, furthermore, that the Orlicz function space equipped with this norm $\left\{ {{L_{\Phi ,{\Phi _{\rm{1}}}}},{{\left\| \cdot \right\|}_{\Phi ,{\Phi _1}}}} \right\}$ is a Banach space. Hence, this paper demonstrates the conditions for the Orlicz space with the Φ-Amemiya norm to contain an asymptotically isometric copy of c0.

Key words： Orlicz space; Amemiya norm; condition Δ2; order asymptotically isometric copy of c0

参考文献

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